Engagement of a lockup clutch is normally permitted when the water temperature of cooling water of an engine is at least 80° C. since, if the lockup clutch is engaged when the oil temperature of hydraulic oil of a transmission is low and the viscosity is high, there are problems such as vibration being generated due to engagement shock; an arrangement in which engagement of a lockup clutch is permitted when the water temperature is less than 80° C. but at least 60° C. and the oil temperature is at least 50° C. to thus increase the frequency of engagement of the lockup clutch and improve the fuel economy is known from Patent Document 1 below.